## Pythagorean Identity

$$
\sin^2\theta + \cos^2\theta \equiv 1
$$

## Pythagorean Identity 2

From the diagram below, we can see that the triangle has horizontal and vertical sides of length $\sin(\theta)$ and $\cos(\theta)$. We now note that the triangle is a right-angled triangle and that the circle has a radius of 1. It follows that $$ (\sin(\theta))^2 + (\cos(\theta))^2 \equiv 1 $$ This is true irrespective of the value of $\theta$